QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo.

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures.

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factor reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10-100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo.

Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. We show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.

Itinerant Antiferromagnetism in RuO_{2}.

Bulk rutile RuO_{2} has long been considered a Pauli paramagnet. Here we report that RuO_{2} exhibits a hitherto undetected lattice distortion below approximately 900 K. The distortion is accompanied by antiferromagnetic order up to at least 300 K with a small room temperature magnetic moment of approximately 0.05µ_{B} as evidenced by polarized neutron diffraction. Density functional theory plus U (DFT+U) calculations indicate that antiferromagnetism is favored even for small values of the Hubbard U of the order of 1 eV. The antiferromagnetism may be traced to a Fermi surface instability, lifting the band degeneracy imposed by the rutile crystal field. The combination of high Néel temperature and small itinerant moments make RuO_{2} unique among ruthenate compounds and among oxide materials in general.

Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo.

Growth in computational resources has lead to the application of real space diffusion quantum Monte Carlo to increasingly heavy elements. Although generally assumed to be small, we find that when using standard techniques, the pseudopotential localization error can be large, on the order of an electron volt for an isolated cerium atom. We formally show that the localization error can be reduced to zero with improvements to the Jastrow factor alone, and we define a metric of Jastrow sensitivity that may be useful in the design of pseudopotentials. We employ an extrapolation scheme to extract the bare fixed node energy and estimate the localization error in both the locality approximation and the T-moves schemes for the Ce atom in charge states 3+ and 4+. The locality approximation exhibits the lowest Jastrow sensitivity and generally smaller localization errors than T-moves although the locality approximation energy approaches the localization free limit from above/below for the 3+/4+ charge state. We find that energy minimized Jastrow factors including three-body electron-electron-ion terms are the most effective at reducing the localization error for both the locality approximation and T-moves for the case of the Ce atom. Less complex or variance minimized Jastrows are generally less effective. Our results suggest that further improvements to Jastrow factors and trial wavefunction forms may be needed to reduce localization errors to chemical accuracy when medium core pseudopotentials are applied to heavy elements such as Ce.

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo.

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

Successes and failures of Hubbard-corrected density functional theory: the case of Mg doped LiCoO2.

We have evaluated the successes and failures of the Hubbard-corrected density functional theory approach to study Mg doping of LiCoO2. We computed the effect of the U parameter on the energetic, geometric, and electronic properties of two possible doping mechanisms: (1) substitution of Mg onto a Co (or Li) site with an associated impurity state and (2) formation of impurity-state-free complexes of substitutional Mg and point defects in LiCoO2. We find that formation of impurity states results in changes on the valency of Co in LiCoO2. Variation of the Co U shifts the energy of the impurity state, resulting in energetic, geometric, and electronic properties that depend significantly on the specific value of U. In contrast, the properties of the impurity-state-free complexes are insensitive to U. These results identify reasons for the strong dependence on the doping properties on the chosen value of U and for the overall difficulty of achieving agreement with the experimentally known energetic and electronic properties of doped transition metal oxides such as LiCoO2.

Polaronic transport and current blockades in epitaxial silicide nanowires and nanowire arrays.

Crystalline micrometer-long YSi2 nanowires with cross sections as small as 1 × 0.5 nm(2) can be grown on the Si(001) surface. Their extreme aspect ratios make electron conduction within these nanowires almost ideally one-dimensional, while their compatibility with the silicon platform suggests application as metallic interconnect in Si-based nanoelectronic devices. Here we combine bottom-up epitaxial wire synthesis in ultrahigh vacuum with top-down miniaturization of the electrical measurement probes to elucidate the electronic conduction mechanism of both individual wires and arrays of nanowires. Temperature-dependent transport through individual nanowires is indicative of thermally assisted tunneling of small polarons between atomic-scale defect centers. In-depth analysis of complex wire networks emphasize significant electronic crosstalk between the nanowires due to the long-range Coulomb fields associated with polaronic charge fluctuations. This work establishes a semiquantitative correlation between the density and distributions of atomic-scale defects and resulting current-voltage characteristics of nanoscale network devices.

Novel cooperative interactions and structural ordering in H2S-H2.

Hydrogen sulfide (H(2)S) and hydrogen (H(2)) crystallize into a 'guest-host' structure at 3.5 GPa and, at the initial formation pressure, the rotationally disordered component molecules exhibit weak van der Waals-type interactions. With increasing pressure, hydrogen bonding develops and strengthens between neighboring H(2)S molecules, reflected in a pronounced drop in S-H vibrational stretching frequency and also observed in first-principles calculations. At 17 GPa, an ordering process occurs where H(2)S molecules orient themselves to maximize hydrogen bonding and H(2) molecules simultaneously occupy a chemically distinct lattice site. Intermolecular forces in the H(2)S+H(2) system may be tuned with pressure from the weak hydrogen-bonding limit to the ordered hydrogen-bonding regime, resulting in a novel clathrate structure stabilized by cooperative interactions.

Charge-order fluctuations in one-dimensional silicides.

Metallic nanowires are of great interest as interconnects in nanoelectronic devices. They also represent important systems for understanding the complexity of electronic interactions and conductivity in one dimension. We have fabricated exceptionally long and uniform YSi(2) nanowires through self-assembly of yttrium atoms on Si(001). The wire widths are quantized in odd multiples of the Si substrate lattice constant. The thinnest wires represent one of the closest realizations of the isolated Peierls chain, exhibiting van Hove type singularities in the one-dimensional density of states and charge-order fluctuations below 150 K. The structure of the wire was determined through a detailed comparison of scanning tunnelling microscopy data and first-principles calculations. Quantized width variations along the thinnest wires produce built-in Schottky junctions, the electronic properties of which are governed by the finite size and temperature scaling of the charge-ordering correlation. This illustrates how a collective phenomenon such as charge ordering might be exploited in nanoelectronic devices.

Microstructure and a nucleation mechanism for nanoprecipitates in PbTe-AgSbTe2.

Many recent advances in thermoelectric (TE) materials are attributed to their nanoscale constituents. Determination of the nanocomposite structures has represented a major experimental and computational challenge and eluded previous attempts. Here we present the first atomically resolved structures of high performance TE material PbTe-AgSbTe2 by transmission electron microscopy imaging and density functional theory calculations. The results establish an accurate structural characterization for PbTe-AgSbTe2 and identify the interplay of electric dipolar interactions and strain fields as the driving mechanism for nanoprecipitate nucleation and aggregation.

van der Waals forces: Accurate calculation and assessment of approximate methods in dielectric nanocolloids up to 16 nm.

A microscopic method is used to calculate the van der Waals (VDW) forces between large nanocolloids. We assess the reliability of predictions derived from the most commonly used macroscopic method in practice, the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory combined with the Derjaguin approximation, by calculating the VDW interactions using the "coupled dipole method" (CDM). The CDM, which has demonstrated its ability to calculate VDW interactions for small nanoclusters, accounts for all many-body forces, and it does not assume a continuous, homogeneous dielectric function in each material. It is shown that, out of three explored, one of the routinely assumed properties ("small-separation dominance") of VDW forces predicted from the macroscopic method is generally applicable for large spherical dielectric nanoclusters of diameter 16 nm allowing much more efficient CDM calculations. The failure of two other routinely assumed properties, "infinite-depth approximation" and "sphere-cube analogy," demonstrates that the effect of finite-size and shape is important in nanocolloid systems even at the large size of 16 nm.

A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations.

We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N(2)) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O(N(2)) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN(2)) work and O(MN(2)) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.

Neutral and charged excitations in carbon fullerenes from first-principles many-body theories.

We investigate the accuracy of first-principles many-body theories at the nanoscale by comparing the low-energy excitations of the carbon fullerenes C(20), C(24), C(50), C(60), C(70), and C(80) with experiment. Properties are calculated via the GW-Bethe-Salpeter equation and diffusion quantum Monte Carlo methods. We critically compare these theories and assess their accuracy against available photoabsorption and photoelectron spectroscopy data. The first ionization potentials are consistently well reproduced and are similar for all the fullerenes and methods studied. The electron affinities and first triplet excitation energies show substantial method and geometry dependence. These results establish the validity of many-body theories as viable alternative to density-functional theory in describing electronic properties of confined carbon nanostructures. We find a correlation between energy gap and stability of fullerenes. We also find that the electron affinity of fullerenes is very high and size independent, which explains their tendency to form compounds with electron-donor cations.

Electronic structure of xDNA.

xDNA is an artificial duplex made of natural and benzo-homologated bases. The latter can be seen as a fusion between benzene and a natural base. We have used two different ab initio techniques, one based on B3LYP and a Gaussian expansion of the wave functions, and the other on GGA and plane-waves, to investigate the electronic properties of an xDNA duplex and a natural one with an analogous sequence. The calculations were performed in dry conditions, i.e., H atoms were used to neutralize the charge. It is found that the HOMO-LUMO gap of xDNA is about 0.5 eV smaller than that of B-DNA, independent of the technique used. The pi-pi* gap of xDNA is 1.3 or 1.0 eV smaller than that of B-DNA, depending on whether one uses B3LYP/6-31G or GGA/plane-waves, respectively. An analysis of how saturation changes the electronic properties of the nucleotide pairs that make up these duplexes suggests that different saturation schemes significantly affect the HOMO-LUMO gap value of xDNA and B-DNA. The same is not true for the pi-pi* gap. That xDNA has a smaller pi-pi* gap than B-DNA suggests that xDNA could be a plausible candidate for molecular-wire applications.

Tunable one-dimensional electron gas carrier densities at nanostructured oxide interfaces.

The emergence of two-dimensional metallic states at the LaAlO3/SrTiO3 (LAO/STO) heterostructure interface is known to occur at a critical thickness of four LAO layers. This insulator to-metal transition can be explained through the "polar catastrophe" mechanism arising from the divergence of the electrostatic potential at the LAO surface. Here, we demonstrate that nanostructuring can be effective in reducing or eliminating this critical thickness. Employing a modified "polar catastrophe" model, we demonstrate that the nanowire heterostructure electrostatic potential diverges more rapidly as a function of layer thickness than in a regular heterostructure. Our first-principles calculations indicate that for nanowire heterostructures a robust one-dimensional electron gas (1DEG) can be induced, consistent with recent experimental observations of 1D conductivity at LAO/STO steps. Similar to LAO/STO 2DEGs, we predict that the 1D charge density decays laterally within a few unit cells away from the nanowire; thus providing a mechanism for tuning the carrier dimensionality between 1D and 2D conductivity. Our work provides insight into the creation and manipulation of charge density at an oxide heterostructure interface and therefore may be beneficial for future nanoelectronic devices and for the engineering of novel quantum phases.

Structure and growth of quasi-one-dimensional YSi2 nanophases on Si(100).

Quasi-one-dimensional YSi(2) nanostructures are formed via self-assembly on the Si(100) surface. These epitaxial nanowires are metastable and their formation strongly depends on the growth parameters. Here, we explore the various stages of yttrium silicide formation over a range of metal coverages and growth temperatures, and establish a rudimentary phase diagram for these novel and often coexisting nanophases. We identify, in addition to previously identified stoichiometric wires, several new nanowire systems. These nanowires exhibit a variety of surface reconstructions, which sometimes coexist on a single wire. From a comparison of scanning tunneling microscopy images, tunneling spectra, and first-principles density functional theory calculations, we determine that these surface reconstructions arise from local orderings of yttrium vacancies. Nanowires often agglomerate into nanowire bundles, the thinnest of which are formed from single wire pairs. The calculations show that such bundles are energetically favored compared to well-separated single wires. Thicker bundles are formed at slightly higher temperature. They extend over several microns, forming a robust network of conducting wires that could possibly be employed in nanodevice applications.

Accurate static and dynamic properties of liquid electrolytes for Li-ion batteries from ab initio molecular dynamics.

Lithium-ion batteries have the potential to revolutionize the transportation industry, as they did for wireless communication. A judicious choice of the liquid electrolytes used in these systems is required to achieve a good balance among high-energy storage, long cycle life and stability, and fast charging. Ethylene-carbonate (EC) and propylene-carbonate (PC) are popular electrolytes. However, to date, almost all molecular-dynamics simulations of these fluids rely on classical force fields, while a complete description of the functionality of Li-ion batteries will eventually require quantum mechanics. We perform accurate ab initio molecular-dynamics simulations of ethylene- and propylene-carbonate with LiPF(6) at experimental concentrations to build solvation models which explain available neutron scattering and nuclear magnetic resonance (NMR) results and to compute Li-ion solvation energies and diffusion constants. Our results suggest some similarities between the two liquids as well as some important differences. Simulations also provide useful insights into formation of solid-electrolyte interphases in the presence of electrodes in conventional Li-ion batteries.

Structure of YSi(2) nanowires from scanning tunneling spectroscopy and first principles.

Exceptionally long and uniform YSi(2) nanowires are formed via self-assembly on Si(001). The in-plane width of the thinnest wires is known to be quantized in odd multiples of the silicon lattice constant. Here, we identify a class of nanowires that violates the "odd multiple" rule. The structure of the thinnest wire in this category is determined by comparing scanning tunneling spectroscopy measurements with the calculated surface density of states of candidate models by means of the Pendry R-factor analysis. The relative stability of the odd and even wire systems is analyzed via first-principles calculations.

Pseudogap and antiferromagnetic correlations in the hubbard model.

Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.